Given the following vectors in R3, that is: 𝑣1 = (1,2, −1), 𝑣2 = (0,1,1), 𝑣3 = (−1, −4,2) a. Find a basis, the dimension and Cartesian equations of the subspace generated by the above three vectors...

Given the following vectors in R3, that is: 𝑣1 = (1,2, −1), 𝑣2 = (0,1,1), 𝑣3 = (−1, −4,2) a. Find a basis, the dimension and Cartesian equations of the subspace generated by the above three vectors...

E(x,y) = (x+2, y-3) and F(x,y) = 2y-x

H={[a,b,c,d]: a+3b=c, b+c+a=d} Show the subset H is a subspace or give a counter example I am very confused can someone help

Determine whether the given set is a subspace of P3. Explain why. A = {p(t) = at^3+bt} Where a and b are both elements of the Reals.

Given a 4x4 matrix where R1: a b c d, R2: e f g h, R3: i j k l, R4: m n o p. We know that the determinant of this matrix is 9. What would the new determinant be if the matrix was transformed into...

How to determine whether the vectors u:(1,-1,4) , v:(-2,1,3) , w:(4,-3,5) span R^3 ???

Per example, these are operators that do not preserve the addition: Ln (a+b) is not = ln a + ln b like (a+b)^3 is not = a^3 + b^3 Maybe...

Please Help! An approximate linear model that gives the remaining distance, in miles, a plane must travel from San Diego to Brussels is given by the function: s(t) = 6000 - 500t (12hrs) where s(t)...

Let T: R2→R2 be the linear transformation that first rotates points clockwise through 30∘ and then reflects points through the line y=x. Find the standard matrix A for T. A = [] ?...

Assume u4 is not a linear combination of {u1,u2,u3} A. {u1,u2,u3,u4} is never a linearly dependent set of vectors. B. {u1,u2,u3,u4} could be a linearly independent or linearly...

Prove that a subset W of a vector space V is a subspace of V if and only if W ≠empty and whenever a∈ F and x,y ∈W then ax∈W and x+y∈W

x,y,z ∈ ℝ3 and x+y+3z=0 How do I prove ax+by+cz=dx+ey, if d and e are real numbers chosen to fit the equation? Thank you very much if...

http://i.imgur.com/PknZsfZ.png I'm confused on why the first row has values 0 + yk+1 + 0 and the second row has 0 + 0 + yk+2

the vector [-14,-7,19] is a linear combination of vectors [-3,-3,-3] and [10,9,-10] if and only if the matrix equation Ax = b has a solution x where A = [? ?] and...

Consider the following system X1+X2+X3=-1 -X1 =-1 X1+X2-X3 =-1 Without solving the system, can you tell if...

The machine can stuff a batch of envelopes in 5 hours. How long would it take the machines to stuff 10 batches of envelopes? 14 batches of envelopes? I know one equation...

The choices are ( A + B , B transpose + A transpose , AB(transpose) , AB. I know that A + B and B transpose + A transpose is wrong. My teacher said that AB is the correct answer but...

Suppose that u•(vxw) = 3 , find u•( wxv) . Please give everyone a detailed explanation on how to solve !

x1 + x2 + 2x3 + 2x4 = 0 x1 + 2x2 + x3 + 3x4 = 0 x1 + 3x2 + 4x4 = 0

I have no idea what Im doing wrong but I keep getting the wrong answer. What I did first was find two points. So I set z=0 and x=0 . Then I created two vectors and did the cross product for ABxAC...